Common imaging device acquires an image by recording the light intensity and the position of a certain point on an observation object. When the light intensity of the observation object is attenuated to a certain extent and reaches a single-photon level, discrete pulse signals are formed. A single photon, as an ultra-weak light, is regarded as the indivisible minimum energy unit of light, the detectable limit as well. The single-photon detection technology is applied in the fields of biological self-illumination, medical diagnosis, nondestructive material analysis, astronomical observation, spectral measurement, quantum optics and the like, and plays an important role therein. Research of ultra-weak light imaging detection technology is very significant for the development of these fields.
Photon counting imaging is an ultra-weak light detection technology. An image is acquired by accumulation and fusion at a data processing end generally through recording photon counting of an imaging position and the probability of detecting photons. The core of the technology is an array detector. The scale (array size), the sensitivity range and the wavelength response range of the array detector directly affect whether the image acquisition quality at single-photon level can be acquired or not. However, the array detector for the single-photon detection level is expensive and can be realized in only a few wave bands, and furthermore it has weak sensitivity, and so there exists the contradiction between technical immaturity and strong demand of two-dimensional imaging of an ultra-weak light object.
The compressed sensing theory (CS theory) was proposed by E. J. Candès et al., which breaks through the traditional linear sampling pattern, and shows that a few measurements of the linear random projection of compressive signals contains enough information for original signal reconstruction.
The CS theory comprises two parts, namely compressive sampling and sparse reconstruction.
The compressive sampling is a process for mapping measured signals from a high dimension to a low dimension. If xεRn is the data to be measured, yεRk is the observation data, ΦεRk×n is a random projection matrix (k<<n) and eεRk is measurement noise, then the compressive sampling process can be described as formula (1):y=Φx+e  (1)
If x is sparse in a transform domain, that is, θ=Ψx and Ψ is a sparse transform matrix, formula (1) is transformed into formula (2):y=ΦΨ−1θ+e  (2)
The random projection matrix Φ is also referred to as a measurement matrix, and is required to satisfy RIP (Restricted Isometry Property):(1−δs)∥x∥22≦∥Ax∥22≦(1+δs)∥x∥22 wherein δs is defined as the minimum constant that leads to all s-sparse vectors x satisfy the above inequality, and the δs<1.
In addition, the more irrelevant between Φ and Ψ is, the smaller the value of the measurement times k required by the sampling is, so generally the Φ is designed as a random matrix.
The sparse reconstruction actually means to solve x in formula (1) under the condition that the observation data Y and the measurement matrix Φ are known, which is an ill-posed problem and generally solved by using an optimization method and can be described as formula (3):
                              min                      x            ∈                          R              n                                      ⁢                  (                                                    1                2                            ⁢                                                                                      y                    -                                          Φ                      ⁢                                                                                          ⁢                      x                                                                                        2                2                                      +                          τ              ⁢                                                                  x                                                  1                                              )                                    (        3        )            
If x is sparse in the transform domain, the reconstruction problem corresponding to formula (2) can be described as formula (4):
                              min                      x            ∈                          R              n                                      ⁢                  (                                                    1                2                            ⁢                                                                                      y                    -                                          Φ                      ⁢                                                                                          ⁢                      x                                                                                        2                2                                      +                          τ              ⁢                                                                                      Ψ                    ⁢                                                                                  ⁢                    x                                                                    1                                              )                                    (        4        )            
In formula (3) and formula (4), the first item is a least-square constraint marked as f(x); the second item is a constraint which describes the sparsity of x; and the sum of the two items is a final target function marked as φ(x).
The DLP technology was proposed by Texas Instruments (TI) and combined with digital video or graphical signals, in which the micro-mirror and lens system can reflect digital images onto a screen or other surfaces. The core of the technology is a DLP chip, namely digital micro-mirror device (DMD control system for short), which is the most precise optical switch in the world now. The DMD control system comprises a matrix of up to 2 million micro-mirrors installed on a hinge, the size of each micro-mirror is smaller than one fifth of the width of human hair, and each micro-mirror can swing in a certain angle range (generally −12° and +12°), these two states being marked as 0 and 1. The micro-mirrors are driven to jitter at a high speed between 0 and 1 by using pulse width modulation (PWM), so that gray-level modulation can be realized. The DMD control system and related precise electronic elements constitute the so-called DLP technology, and the DLP technology has mature products which are widely applied to products such as projectors.
According to the spirit of “sampling first and reconstructing subsequently”, it is possible to convert two-dimensional signals into one-dimensional signals in time sequence and to do the sampling by using a single detector. The point detector has a wider selection range in terms of both detection sensitivity and wavelength range, with the advantage of low cost and so single-photon counting imaging realized by using the point detector becomes an important development tendency of future single-photon level imaging.